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Regex to find and remove char with specific pattern

I have this string
This is mail#mail.text #1 but page is #001#
(001 is variable, ex 01a or 021 etc)
And I want to make it
This is mail#mail.text #1 but page is 001
With this ^#([0-9]{1,3})#\z i can find a string that starts with "#" and ends with "#" with max 3 chars inside but it doesn't match inside a entire text.

You need to remove ^ (start of the string anchor) and replace the match with the contents of Group 1 using $1 backreference:
var str = "This is mail#mail.text #1 but page is #001#";
var result = Regex.Replace(str, #"#([0-9]{1,3})#\z", "$1");
See the regex demo
The #([0-9]{1,3})#\z pattern will find #, 1 to 3 digits (put inside a group), and then a # at the very end of string (\z).
Another variation: if the value may start with a digit and can be followed with an ASCII letter or digit, use
var result = Regex.Replace(str, #"#([0-9][0-9a-zA-Z]{0,2})#\z", "$1");
And if the value can just be alphanumeric, just use
var result = Regex.Replace(str, #"#([0-9a-zA-Z]{1,3})#\z", "$1");

Split constantly on the last delimiter in C#

I have the following string:
string x = "hello;there;;you;;;!;"
The result I want is a list of length four with the following substrings:
"hello"
"there;"
"you;;"
"!"
In other words, how do I split on the last occurrence when the delimiter is repeating multiple times? Thanks.

You need to use a regex based split:
var s = "hello;there;;you;;;!;";
var res = Regex.Split(s, #";(?!;)").Where(m => !string.IsNullOrEmpty(m));
Console.WriteLine(string.Join(", ", res));
// => hello, there;, you;;, !
See the C# demo
The ;(?!;) regex matches any ; that is not followed with ;.
To also avoid matching a ; at the end of the string (and thus keep it attached to the last item in the resulting list) use ;(?!;|$) where $ matches the end of string (can be replaced with \z if the very end of the string should be checked for).

It seems that you don't want to remove empty entries but keep the separators.
You can use this code:
string s = "hello;there;;you;;;!;";
MatchCollection matches = Regex.Matches(s, #"(.+?);(?!;)");
foreach(Match match in matches)
{
Console.WriteLine(match.Captures[0].Value);
}

string x = "hello;there;;you;;;!;"
var splitted = x.Split(new char[] { ';' }, StringSplitOptions.RemoveEmptryEntries);
foreach (var s in splitted)
Console.WriteLine("{0}", s);

Extract string that contains only letters in C#

string input = "5991 Duncan Road";
var onlyLetters = new String(input.Where(Char.IsLetter).ToArray());
Output: DuncanRoad
But I am expecting output is Duncan Road. What need to change ?

For the input like yours, you do not need a regex, just skip all non-letter symbols at the beginning with SkipWhile():
Bypasses elements in a sequence as long as a specified condition is true and then returns the remaining elements.
C# code:
var input = "5991 Duncan Road";
var onlyLetters = new String(input.SkipWhile(p => !Char.IsLetter(p)).ToArray());
Console.WriteLine(onlyLetters);
See IDEONE demo
A regx solution that will remove numbers that are not part of words and also adjoining whitespace:
var res = Regex.Replace(str, #"\s+(?<!\p{L})\d+(?!\p{L})|(?<!\p{L})\d+(?!\p{L})\s+", string.Empty); 

You can use this lookaround based regex:
repl = Regex.Replace(input, #"(?<![a-zA-Z])[^a-zA-Z]|[^a-zA-Z](?![a-zA-Z])", "");
//=> Duncan Road
(?<![a-zA-Z])[^a-zA-Z] matches a non-letter that is not preceded by another letter.
| is regex alternation
[^a-zA-Z](?![a-zA-Z]) matches a non-letter that is not followed by another letter.
RegEx Demo

You can still use LINQ filtering with Char.IsLetter || Char.IsWhiteSpace. To remove all leading and trailing whitespace chars you can call String.Trim:
string input = "5991 Duncan Road";
string res = String.Join("", input.Where(c => Char.IsLetter(c) || Char.IsWhiteSpace(c)))
.Trim();
Console.WriteLine(res); // Duncan Road

Check multiple words in a string using Contains method

I want to check multiple words in a string and want to replace them. Suppose that my string is
str= 20148(R)/(work)24553(r)
if(str.contains(("R)" || str.Contains("(work)"))
{
//Here I have to replace (R) and (Work) with space "".
// so that my string should be like this 20148/24553
}
How can check multiple words not by using loops, and in one flow.
I am new to c#. Please help me out

You don't need the if, just do:
var newStr = str.Replace("(R)"," ").Replace("(work)"," ");
If you want a space as you say or:
var newStr = str.Replace("(R)",string.Empty).Replace("(work)",string.Empty);
If you want an empty string.

Put R and r inside a character class to match both letters.
string str = "20148(R)/(work)24553(r)";
string result = Regex.Replace(str, #"\((?:[Rr]|work)\)", "");
Console.WriteLine(result);
IDEONE
OR
string str = "20148(R)/(work)24553(r)";
string result = Regex.Replace(str, #"(?i)\((?:R|work)\)", "");
Console.WriteLine(result);
IDEONE
Pattern Explanation:
(?i) (i modifier) would turn on the case-insensitive mode. So it would match both upper and lowercase letters.
\( Matches a literal ( symbol.
(?:) Non-capturing group.
R|work Matches a letter R or string work.(case-insensitive match)
\) Matches a literal ) symbol.

You could use the Regex.Replace method.
string str = "20148(R)/(work)24553(r)";
string str2 = Regex.Replace(str, "[(](?:R|work)[)]", "", RegexOptions.IgnoreCase);
Console.Writeline(str2); //prints 20148/24553
This says take the string str and match the pattern [(R|work)] and replace any instances with "" ignoring the case of the input string when doing the comparison (so it matches (R) and (r)).

With regex you can replace this
[(]\b(?:R|work)\b[)]
With empty string ""
Edit:
string str1 = "20148(R)/(work)24553(r)";
string str2 = Regex.Replace(str1, "[(]\b(?:R|work)\b[)]", "", RegexOptions.IgnoreCase);
Console.Writeline(str2);

C# Why i can not split the string?

string myNumber = "3.44";
Regex regex1 = new Regex(".");
string[] substrings = regex1.Split(myNumber);
foreach (var substring in substrings)
{
Console.WriteLine("The string is : {0} and the length is {1}",substring, substring.Length);
}
Console.ReadLine();
I tried to split the string by ".", but it the splits return 4 empty string. Why?

. means "any character" in regular expressions. So don't split using a regex - split using String.Split:
string[] substrings = myNumber.Split('.');
If you really want to use a regex, you could use:
Regex regex1 = new Regex(#"\.");
The # makes it a verbatim string literal, to stop you from having to escape the backslash. The backslash within the string itself is an escape for the dot within the regex parser.

the easiest solution would be: string[] val = myNumber.Split('.');

. is a reserved character in regex. if you literally want to match a period, try:
Regex regex1 = new Regex(#"\.");
However, you're better off simply using myNumber.Split(".");

The dot matches a single character, without caring what that character
is. The only exception are newline characters.
Source: http://www.regular-expressions.info/dot.html
Therefore your implying in your code to split the string at each character.
Use this instead.
string substr = num.Split('.');

Keep it simple, use String.Split() method;
string[] substrings = myNumber.Split('.');
It has an other overload which allows specifying split options:
public string[] Split(
char[] separator,
StringSplitOptions options
)

You don't need regex you do that by using Split method of string object
string myNumber = "3.44";
String[] substrings = myNumber.Split(".");
foreach (var substring in substrings)
{
Console.WriteLine("The string is : {0} and the length is {1}",substring, substring.Length);
}
Console.ReadLine();

The period "." is being interpreted as any single character instead of a literal period.
Instead of using regular expressions you could just do:
string[] substrings = myNumber.Split(".");

In Regex patterns, the period character matches any single character. If you want the Regex to match the actual period character, you must escape it in the pattern, like so:
#"\."
Now, this case is somewhat simple for Regex matching; you could instead use String.Split() which will split based on the occurrence of one or more static strings or characters:
string[] substrings = myNumber.Split('.');

try
Regex regex1 = new Regex(#"\.");
EDIT: Er... I guess under a minute after Jon Skeet is not too bad, anyway...

You'll want to place an escape character before the "." - like this "\\."
"." in a regex matches any character, so if you pass 4 characters to a regex with only ".", it will return four empty strings. Check out this page for common operators.

Try
Regex regex1 = new Regex("[.]");